Cut -off Frequency is

Rectangular Waveguide and TE11 Mode

A rectangular waveguide is a type of transmission line used for guiding electromagnetic waves, typically in the microwave frequency range. It is characterized by its rectangular cross-section, with two sides of unequal length. The TE11 mode is the fundamental mode of operation for a rectangular waveguide, where the electric field is transverse to the direction of propagation and has only one variation across the cross-section.

Calculating the Minimum Operating Frequency

To determine the minimum operating frequency for the TE11 mode in a rectangular waveguide, we can use the cutoff frequency equation. The cutoff frequency is the frequency below which the waveguide cannot support the propagation of the desired mode. In this case, we want to find the cutoff frequency for the TE11 mode.

The cutoff frequency equation for the TE11 mode in a rectangular waveguide is given by:

fc = c / (2 * sqrt(a^2 + b^2))

Where:
- fc is the cutoff frequency
- c is the speed of light in a vacuum (3 * 10^8 m/s)
- a and b are the internal dimensions of the waveguide

Substituting the Given Values

In this problem, the internal dimensions of the rectangular waveguide are given as a = 4 cm and b = 3 cm. We need to convert these dimensions to meters before substituting them into the equation.

a = 4 cm = 0.04 m
b = 3 cm = 0.03 m

Substituting these values into the cutoff frequency equation, we get:

fc = (3 * 10^8 m/s) / (2 * sqrt((0.04 m)^2 + (0.03 m)^2))

Simplifying the equation further:

fc = (3 * 10^8 m/s) / (2 * sqrt(0.0016 m^2 + 0.0009 m^2))
= (3 * 10^8 m/s) / (2 * sqrt(0.0025 m^2))
= (3 * 10^8 m/s) / (2 * 0.05 m)
= (3 * 10^8 m/s) / 0.1 m
= 3 * 10^9 Hz

Converting the frequency to decimal places:

fc = 3 * 10^9 Hz = 3,000,000,000 Hz = 3,000 MHz

Therefore, the minimum operating frequency for the TE11 mode in this rectangular waveguide is 3 GHz. The answer given as '6.25' is incorrect.